(i)[1]
Find the vector $\overrightarrow{DF}$.
(ii)[3]
Find the unit vector that points in the direction of $\overrightarrow{EF}$.
(iii)[4]
Use a scalar product to determine angle $EFD$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a solid figure $OABCDEF$ with a horizontal rectangular base $OABC$, where $OA = 6$ units and $AB = 3$ units. The vertical edges $OF$, $AD$ and $BE$ measure $6$ units, $4$ units and $4$ units respectively. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OF$ respectively.